Variance Reduction Technique for a Cellular System with Dynamic Resource Sharing

A new algorithm is given to improve the simulation of a cellular system with dynamic resource sharing. This technique is based on low discrepancy sequences, used in quasi-Monte Carlo methods and which, combined with Monte Carlo techniques using importance sampling and control variates (already developed for such a system), gives the best known results. INTRODUCTION We consider a cellular system with dynamic resource sharing, used in digital cellular phone networks. The models used to evaluate such systems generally lead to product-form solutions, but analytic computation is intractable due to the size of the state space. An alternative way is the use of probabilistic methods, that is of Monte Carlo methods. Such techniques are commonly used in various research areas. In the same way, deterministic methods, called quasi-Monte Carlo methods use low discrepancy sequences. Unfortunately, in practice, an error bound for these approaches is uncomputable. We then use low discrepancy sequences as a variance reduction method. In this paper, we first briefly describe the model and the solutions developed in (Fleming and Schaeffer 1995). Next, we develop a new variance reduction technique based on low discrepancy sequences. Finally, we give a numerical illustration of the improvement on a simple example.